Current Courses (Duke University):
Courses taught at Virginia Tech:
Courses taught at Bashkir State University:
TEACHING PHILOSOPHY
If I were to extract a conclusion from my teaching experience over the last eight years, it would be that respect for students and deep knowledge of the subject are the key factors in effective teaching. Respect for students means a careful preparation of the material, making lectures more accessible and interactive, and willing to help students with any questions they may have in the class and during office hours. The teacher's deep knowledge of the subject makes lectures easy for anyone to learn.
My teaching approach has the following major features. First, information presented in my lectures is taken from the textbook assigned for a given course and a variety of other sources including recent research publications. The material taken from other sources is handed out to students and posted on the course website. In my lectures I try to engage students by using historical remarks and examples from different fields of science. I bring a lot of energy and excitement to the classroom, striving to keep my students learning, interested and motivated.
Second, teaching tools used in my lectures include overhead projector, computer projector, and blackboard. The most important definitions are given on transparencies. Blackboard is used for interim calculations and examples. The computer projector serves to show animated images and other information about physical and biological processes and phenomena associated with them. The number of slides used in each class is six or less. In this case, students will have sufficient time to read the slides and take notes.
Third, the slides are posted on the course website (in the section "Online lectures") after class. To my mind, having the lectures online helps students and makes learning more attractive, especially for undergraduates.
Fourth, my priority is to help students in need. I always come in to the classroom before class time and stay in the classroom several minutes after class ended (to answer students' questions). My students are encouraged to discuss academic and personal questions with me during regular office hours or by email. I receive many emails from the students with questions and appointment requests and do my best to reply to them properly. The websites of my courses usually contain a lot of information and advice for homework. I carefully correct all homework problems of each student, explaining mistakes and showing the correct solution, if needed.
Finally, my deep knowledge of the subject is confirmed by students' comments and evaluations.
TEACHING EXPERIENCE
My teaching experience has been interdisciplinary. I taught Higher Mathematics (Calculus), Nonlinear Waves, Mathematical Methods in Mechanics, Numerical Methods, Computer Technologies, Programming Languages, and Introduction to Computers at Bashkir State University (Ufa, Russia); Introduction to Differential Equations (MATH 2214), Multivariable Calculus(MATH 2224), and Vector/Complex Analysis for Engineers (MATH 4574) at Virginia Tech. I gave several lectures on cell adhesion in the framework of the graduate course "Transport Phenomena in Cells and Organs" (BME 216) at Duke University. In Spring 2005 I will teach a graduate-level course "Cell Biomechanics" for biomedical engineering students at Duke.
I started teaching in Fall 1996 as Graduate Teaching Assistant in the Department of Mathematics at Bashkir State University. The first course that I taught was Computer Technologies. It is designed for juniors specializing in Applied Mathematics, lasts one year (both Fall and Spring semesters) and covers such topics as mathematical typesetting with LaTeX, scientific graphics, introduction to modern mathematical software (Matlab, Maple, Mathematica) and introduction to databases (FoxPro, Access). The course provided necessary skills for computer-oriented research. I taught this course also in 1997-1998. In Spring 1996-1998 I assisted Professor Iskander Sh. Akhatov with lectures on Nonlinear Waves, a one-semester course for applied math seniors. In this course the basic concepts and definitions of nonlinear wave theory are discussed, including nonlinear wave processes, soliton equations (Korteveg-de Vries, nonlinear Schrodinger, sin-Gordon, Kadomzev-Petviashvili and Davey-Stewartson equations), direct and inverse methods for their solutions (Hirota method, Backlund and inverse scattering transforms), and asymptotic derivation of nonlinear evolution equations. My part was to show how the Korteveg-de Vries and nonlinear Schrodinger equations could be derived from the equations of motion of a bubbly liquid and of a free-collision plasma. These lectures were based on my PhD work. I taught Nonlinear Waves entirely on my own in Spring 1999-2000.
Beginning in Spring 1999 I started an appointment as Assistant Professor of Applied Mathematics at Bashkir State University. I was an instructor for Higher Mathematics and Nonlinear Waves in that semester. Higher Mathematics (US analog is Calculus) is a two-year course for beginning engineering majors. During the first year, students (freshmen) study Elementary Calculus (real and complex functions, polynomials), Analytic Geometry, Differential Calculus (limits, continuity, differentiation), and Integral Calculus. During the second year, they study Multivariable Calculus (functions of several variables, multiple integrals, series), Ordinary Differential Equations, and Probability Theory. Higher Mathematics is the basic math course for engineering majors in Russia. I continued to teach this course in Fall 1999 and Spring 2000.
In Fall 1999 I was an instructor for Mathematical Methods in Mechanics, a one-semester course for applied math juniors, with topics such as perturbation methods, dynamical systems, and theory of chaos. The course was developed by me and its significant part was from my master's and graduate theses (strange attractors, method of multiple scales, acoustics of bubbly liquids, and sonoluminescence). I also taught, together with Prof. Vakhitova, a course on Numerical Methods for applied math seniors in Spring 2000. We covered the Runge-Kutta, predictor-corrector, Krank-Nikolson, alternating-direction, and Godunov methods.
In Virginia Tech I taught three undergraduate courses: "Introduction to Differential Equations" (Spring 2002, First Summer Session of 2003), "Multivariable Calculus" (Spring 2002), and "Vector/Complex Analysis for Engineers" (First Summer Session of 2002). If you click here, you can find the course contract and a list of online lectures for "Introduction to Differential Equations". Here is the information about "Vector/Complex Analysis for Engineers".
TEACHING PLANS
I am qualified and would enjoy developing and teaching graduate-level courses in cell biomechanics, transport phenomena in cells and organs, and medical ultrasound. I would also enjoy teaching multiphase flow, dynamics of bubbles and drops, fluid dynamics, continuous media mechanics, nonlinear acoustics, numerical methods, asymptotic methods, differential equations, multivariable calculus, vector/complex analysis and other mathematical courses designed for engineers. My vision for the graduate-level bioengineering courses is described below.
Cell biomechanics: Fundamental principles of continuum mechanics will be applied to problems of biomechanics at the cellular level. This one-semester course will discuss structure of mammalian cells, models of cell viscoelasticity, surface rheology of the cell membrane, flow-induced deformation of blood cells (leukocytes, erythrocytes, and platelets), cell adhesion, and experimental techniques (micropipette aspiration, biointerface probe, atomic force microscopy, parallel-plate flow chamber).
Transport phenomena in cells and organs: Fundamental principles of fluid mechanics and mass transport (diffusion, convection) will be applied to physiological problems. The topics of this two-semester course will be the cardiovascular system (pulmonary and systemic circulations, structure of blood vessels), the respiratory system, rheology of blood flow, transmembrane and transvascular transport (including gas transport between blood and tissues), transport within the cell, cell adhesion, and medical applications (inflammation, atherosclerosis, cancer metastasis, sickle cell disease, and pulmonary embolism).
Medical ultrasound: This one-semester course will be devoted to medical applications of ultrasound. It will cover ultrasound imaging (B-mode, Doppler mode, contrast-enhanced imaging, nonlinear imaging), high-intensity focused ultrasound (hyperthermia, lithotripsy), acoustic cavitation and its bioeffects, and ultrasound-assisted delivery of drugs and genes.
STUDENTS' COMMENTS ABOUT MY TEACHING